Decadal buoyancy forcing in a simple model of the subtropical gyre

The decadal response of the ventilated thermocline to surface buoyancy forc ing is investigated, using simplified mixed layer thermodynamics and two-la yer planetary geostrophic dynamics. The model is forced by a stationary Ekm an pumping and a fluctuating sea surface density, while the associated surf ace buoyancy flux is diagnosed from the buoyancy budget of ventilated colum ns. The decadal forcing is represented as a slow modulation of the seasonal cycle, rather than a slow periodic forcing as in Liu and Pedlosky. It is f ound that the amplitude and the degree of nonlinearity of the interior resp onse depend on the anomalies of the yearly averaged surface buoyancy flux, but that omitting the seasonal cycle leads to an overestimation of the ther mocline variability by a factor of 2. At periods longer than 10 years. the interior response becomes linear and frequency independent so that in the p resence of stochastic buoyancy forcing the spectrum of potential vorticity or interface displacement is white at low frequency and red at high frequen cy. A statistical signature of the buoyancy forcing is the asymmetric shape of the cross-covariance function between sea surface density and interface displacement anomalies in lead and lag conditions.